Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alqx)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-5/2

http://functions.wolfram.com/07.25.03.alqx.01

Input Form

HypergeometricPFQ[{7/2, 6}, {-(5/2), -(1/2)}, -z] == (1/3375) (3375 - 56700 z - 1190700 z^2 - 23284800 z^3 + 154285560 z^4 - 235778400 z^5 + 149320860 z^6 - 47705400 z^7 + 8396895 z^8 - 841088 z^9 + 47280 z^10 - 1376 z^11 + 16 z^12) + (1/6750) ((Sqrt[Pi] (118146600 z^(7/2) - 463834800 z^(9/2) + 588147300 z^(11/2) - 339672240 z^(13/2) + 103072785 z^(15/2) - 17590890 z^(17/2) + 1728120 z^(19/2) - 95920 z^(21/2) + 2768 z^(23/2) - 32 z^(25/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]